What's the cheapest way to move boxes across the country?

Look into commercial freight. Depending on where you both are, UPS Freight and FedEx Freight both have good rates.

USPS’s parcel post would be the cheapest.

Rail freight can be cheaper and easier, depending on where you’re shipping from and to. But if it is not a huge number of boxes, and he is going to be flying back and forth for visits, then it is definitely cheapest to pack for carryon and check some of the boxes through as luggage back on his way home.

Great question. I’m going to be moving my stuff from Kansas to New York fairly soon as well. @Mamradpivo and @wildpotato could you guys tell me a bit more about freight shipping? Is it just a large box? Does someone deliver and pick it up from your house? Do they just drop it off at the place you tell them to? Do you know how long it takes? Or if you could point me in the right direction with a good link, that would also be great! Thanks!

Look at Shipgooder.

You enter the origination and destination zip codes, weight, box size etc and it will tell you the best way to go. Enjoy!

A few years ago I shipped a bunch of my stuff by Gator Freight (linked to Yellow Freight).

They picked it up from my house, requiring only that I a) be there when they came to sign the shipping documents and b) there was access by an 18-wheeler. They delivered it at the destination very quickly (Florida to Arizona in three days), requiring a) that someone be there to accept the shipment, and b) there was access by an 18-wheeler. Since it took me longer to get there than the truck did I had the stuff delivered to the University where a departmental secretary signed for it. It was stashed in the basement of the Biology building next to the loading dock.

Be aware that if you ship by a commercial freight line like Yellow Freight that:

There is no insurance.
They can’t tell you precisely when it will get there.
They don’t tote things long distances – they want it next to the truck access and will use a dolly only if they have to.
If no one is there to sign for it delivery won’t happen (although sometimes they are ingenious about finding random strangers to take possession).
Your boxes need to tolerate being thrown up to 10 feet, or dropped off the back end of the truck.

I shipped 2000 pounds of books for $1.00 a pound, which is even cheaper than Media Mail. It would have cost me $9000 to use a moving company, even without packers.

However, if you just have a few boxes, then the post office will be cheapest, but UPS or FedEx will have better tracking.